Horizon Explorer’s last ability will trigger once for each player you attack.

If a land has an ability that says it enters tapped, you choose the order in which that ability’s effect and the effect of Horizon Explorer’s first ability apply. This means you can choose to have the land enter tapped or untapped. If a land you control is simply put onto the battlefield tapped without a replacement effect being applied, it always enters untapped if you control Horizon Explorer.